A Different Approach to High-Tc Superconductivity: Indication of Filamentary-Chaotic Conductance and Possible Routes to Room Temperature Superconductivity

Abstract

The empirical relation of between the transition temperature of optimum doped superconductors T co and the mean cationic charge , a physical paradox, can be recast to strongly support fractal theories of high-T c superconductors, thereby applying the finding that the optimum hole concentration of σ o = 0.229 can be linked with the universal fractal constant δ 1 = 8.72109… of the renormalized quadratic Hénon map. The transition temperature obviously increases steeply with a domain structure of ever narrower size, characterized by Fibonacci numbers. However, also conventional BCS superconductors can be scaled with δ 1 , exemplified through the energy gap relation k B T c ≈ 5Δ 0 /δ 1 , suggesting a revision of the entire theory of superconductivity. A low mean cationic charge allows the development of a frustrated nano-sized fractal structure of possibly ferroelastic nature delivering nano-channels for very fast charge transport, in common for both high-T c superconductor and organic-inorganic halide perovskite solar materials. With this backing superconductivity above room temperature can be conceived for synthetic sandwich structures of less than 2+. For instance, composites of tenorite and cuprite respectively tenorite and CuI (CuBr, CuCl) onto AuCu alloys are proposed. This specification is suggested by previously described filamentary superconductivity of “bulk” CuO1 ﹣ x samples. In addition, cesium substitution in the Tl-1223 compound is an option.